MinT - Best Known (195−134, 195, s)-Nets in Base 4

Best Known (195−134, 195, s)-Nets in Base 4

(195−134, 195, 66)-Net over F₄ — Constructive and digital

Digital (61, 195, 66)-net over F₄, using

t-expansion [i] based on digital (49, 195, 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]

(195−134, 195, 99)-Net over F₄ — Digital

Digital (61, 195, 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]

(195−134, 195, 432)-Net in Base 4 — Upper bound on s

There is no (61, 195, 433)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2591 458694 136506 313628 614008 679460 354550 235291 747404 568458 489713 692764 639419 756718 901071 190721 278747 620982 632441 746912 > 4¹⁹⁵ [i]