MinT - Best Known (196−128, 196, s)-Nets in Base 4

Best Known (196−128, 196, s)-Nets in Base 4

(196−128, 196, 66)-Net over F₄ — Constructive and digital

Digital (68, 196, 66)-net over F₄, using

t-expansion [i] based on digital (49, 196, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(196−128, 196, 99)-Net over F₄ — Digital

Digital (68, 196, 99)-net over F₄, using

t-expansion [i] based on digital (61, 196, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(196−128, 196, 522)-Net in Base 4 — Upper bound on s

There is no (68, 196, 523)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10131 590245 417577 133893 080366 037477 718648 120889 555203 563039 119275 498825 055262 807610 319771 948319 170038 492966 032423 173816 > 4¹⁹⁶ [i]