MinT - Best Known (65, 65+114, s)-Nets in Base 4

Best Known (65, 65+114, s)-Nets in Base 4

(65, 65+114, 66)-Net over F₄ — Constructive and digital

Digital (65, 179, 66)-net over F₄, using

t-expansion [i] based on digital (49, 179, 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]

(65, 65+114, 99)-Net over F₄ — Digital

Digital (65, 179, 99)-net over F₄, using

t-expansion [i] based on digital (61, 179, 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]

(65, 65+114, 526)-Net in Base 4 — Upper bound on s

There is no (65, 179, 527)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 609670 797582 670709 349962 317933 070481 750204 209366 397784 434952 433663 160067 747025 974301 076366 784496 898315 294400 > 4¹⁷⁹ [i]