MinT - Best Known (185−107, 185, s)-Nets in Base 4

Best Known (185−107, 185, s)-Nets in Base 4

(185−107, 185, 104)-Net over F₄ — Constructive and digital

Digital (78, 185, 104)-net over F₄, using

t-expansion [i] based on digital (73, 185, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(185−107, 185, 112)-Net over F₄ — Digital

Digital (78, 185, 112)-net over F₄, using

t-expansion [i] based on digital (73, 185, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(185−107, 185, 802)-Net in Base 4 — Upper bound on s

There is no (78, 185, 803)-net in base 4, because

1 times m-reduction [i] would yield (78, 184, 803)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 634 504061 655781 516759 841807 925532 254397 499720 739807 743281 382343 119575 700379 279674 804577 043131 703903 386218 154880 > 4¹⁸⁴ [i]