MinT - Best Known (196−100, 196, s)-Nets in Base 4

Best Known (196−100, 196, s)-Nets in Base 4

(196−100, 196, 104)-Net over F₄ — Constructive and digital

Digital (96, 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]

(196−100, 196, 144)-Net over F₄ — Digital

Digital (96, 196, 144)-net over F₄, using

t-expansion [i] based on 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]

(196−100, 196, 1447)-Net in Base 4 — Upper bound on s

There is no (96, 196, 1448)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10325 064496 340791 079540 231064 754318 300679 182084 777612 718878 946753 294742 489563 923534 900237 802716 623089 315567 777670 294328 > 4¹⁹⁶ [i]