MinT - Best Known (95, 95+114, s)-Nets in Base 4

Best Known (95, 95+114, s)-Nets in Base 4

(95, 95+114, 104)-Net over F₄ — Constructive and digital

Digital (95, 209, 104)-net over F₄, using

t-expansion [i] based on digital (73, 209, 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]

(95, 95+114, 144)-Net over F₄ — Digital

Digital (95, 209, 144)-net over F₄, using

t-expansion [i] based on digital (91, 209, 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]

(95, 95+114, 1140)-Net in Base 4 — Upper bound on s

There is no (95, 209, 1141)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 688946 365303 913685 113411 053490 159587 791233 106561 641643 124023 565492 215898 362455 051282 458966 100234 097379 518540 615681 282960 668608 > 4²⁰⁹ [i]