MinT - Best Known (49, 134, s)-Nets in Base 4

Best Known (49, 134, s)-Nets in Base 4

(49, 134, 66)-Net over F₄ — Constructive and digital

Digital (49, 134, 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]

(49, 134, 81)-Net over F₄ — Digital

Digital (49, 134, 81)-net over F₄, using

t-expansion [i] based on digital (46, 134, 81)-net over F₄, using
- net from sequence [i] based on digital (46, 80)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 46 and N(F) ≥ 81, using
    - Drinfeld modules of rank 1 [i]

(49, 134, 410)-Net in Base 4 — Upper bound on s

There is no (49, 134, 411)-net in base 4, because

1 times m-reduction [i] would yield (49, 133, 411)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 126 649193 667332 001047 733149 526887 400663 626751 457619 622943 914360 201463 709323 709620 > 4¹³³ [i]