MinT - Best Known (106−60, 106, s)-Nets in Base 32

Best Known (106−60, 106, s)-Nets in Base 32

(106−60, 106, 202)-Net over F₃₂ — Constructive and digital

Digital (46, 106, 202)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 37, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (9, 69, 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]

(106−60, 106, 362)-Net over F₃₂ — Digital

Digital (46, 106, 362)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−60, 106, 513)-Net in Base 32 — Constructive

(46, 106, 513)-net in base 32, using

2 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]

(106−60, 106, 80824)-Net in Base 32 — Upper bound on s

There is no (46, 106, 80825)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3516 051007 201695 519601 680632 219106 594717 566165 308901 070031 395092 537837 682790 861126 083788 593201 719705 150274 564607 597802 568113 064882 131032 961093 338394 121877 100624 > 32¹⁰⁶ [i]