MinT - Best Known (51, 108, s)-Nets in Base 32

Best Known (51, 108, s)-Nets in Base 32

(51, 108, 240)-Net over F₃₂ — Constructive and digital

Digital (51, 108, 240)-net over F₃₂, using

1 times m-reduction [i] based on digital (51, 109, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 40, 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]
  2. digital (11, 69, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(51, 108, 513)-Net in Base 32 — Constructive

(51, 108, 513)-net in base 32, using

t-expansion [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]

(51, 108, 560)-Net over F₃₂ — Digital

Digital (51, 108, 560)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 108, 205795)-Net in Base 32 — Upper bound on s

There is no (51, 108, 205796)-net in base 32, because

1 times m-reduction [i] would yield (51, 107, 205796)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112479 052944 603327 759673 460435 985779 791727 852474 641604 158213 091082 869615 073049 531062 987305 786465 219396 524291 655432 373471 132117 507051 605172 063916 831856 651295 869304 > 32¹⁰⁷ [i]