MinT - Best Known (97−51, 97, s)-Nets in Base 32

Best Known (97−51, 97, s)-Nets in Base 32

(97−51, 97, 224)-Net over F₃₂ — Constructive and digital

Digital (46, 97, 224)-net over F₃₂, using

1 times m-reduction [i] based on digital (46, 98, 224)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 35, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]
  2. digital (11, 63, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(97−51, 97, 513)-Net in Base 32 — Constructive

(46, 97, 513)-net in base 32, using

11 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(97−51, 97, 527)-Net over F₃₂ — Digital

Digital (46, 97, 527)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−51, 97, 197702)-Net in Base 32 — Upper bound on s

There is no (46, 97, 197703)-net in base 32, because

1 times m-reduction [i] would yield (46, 96, 197703)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 121989 368143 904578 024305 361197 269148 982398 867154 029319 251494 825009 938049 870659 485925 797680 667845 597057 405958 735136 587205 833094 857506 990855 445040 > 32⁹⁶ [i]