MinT - Best Known (196−105, 196, s)-Nets in Base 4

Best Known (196−105, 196, s)-Nets in Base 4

(196−105, 196, 104)-Net over F₄ — Constructive and digital

Digital (91, 196, 104)-net over F₄, using

t-expansion [i] based on digital (73, 196, 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]

(196−105, 196, 144)-Net over F₄ — Digital

Digital (91, 196, 144)-net over F₄, using

net from sequence [i] based on digital (91, 143)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]

(196−105, 196, 1178)-Net in Base 4 — Upper bound on s

There is no (91, 196, 1179)-net in base 4, because

1 times m-reduction [i] would yield (91, 195, 1179)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2617 275404 096071 757396 669949 616473 669162 960174 550025 527904 153491 356235 480902 253719 573664 000060 520761 935799 543907 965720 > 4¹⁹⁵ [i]