MinT - Best Known (67, 67+120, s)-Nets in Base 4

Best Known (67, 67+120, s)-Nets in Base 4

(67, 67+120, 66)-Net over F₄ — Constructive and digital

Digital (67, 187, 66)-net over F₄, using

t-expansion [i] based on digital (49, 187, 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]

(67, 67+120, 99)-Net over F₄ — Digital

Digital (67, 187, 99)-net over F₄, using

t-expansion [i] based on digital (61, 187, 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]

(67, 67+120, 533)-Net in Base 4 — Upper bound on s

There is no (67, 187, 534)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 39873 080372 589566 880373 002836 225594 179969 085506 633090 482183 811365 534683 599325 229826 378551 482473 316525 460307 516480 > 4¹⁸⁷ [i]