MinT - Best Known (74, 74+107, s)-Nets in Base 4

Best Known (74, 74+107, s)-Nets in Base 4

(74, 74+107, 104)-Net over F₄ — Constructive and digital

Digital (74, 181, 104)-net over F₄, using

t-expansion [i] based on digital (73, 181, 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]

(74, 74+107, 112)-Net over F₄ — Digital

Digital (74, 181, 112)-net over F₄, using

t-expansion [i] based on digital (73, 181, 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]

(74, 74+107, 718)-Net in Base 4 — Upper bound on s

There is no (74, 181, 719)-net in base 4, because

1 times m-reduction [i] would yield (74, 180, 719)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 467076 019528 731058 405232 444182 554656 365791 846083 696600 626534 560111 263493 870627 767660 460779 913852 302840 562680 > 4¹⁸⁰ [i]