MinT - Best Known (65, 65+134, s)-Nets in Base 4

Best Known (65, 65+134, s)-Nets in Base 4

(65, 65+134, 66)-Net over F₄ — Constructive and digital

Digital (65, 199, 66)-net over F₄, using

t-expansion [i] based on digital (49, 199, 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+134, 99)-Net over F₄ — Digital

Digital (65, 199, 99)-net over F₄, using

t-expansion [i] based on digital (61, 199, 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+134, 474)-Net in Base 4 — Upper bound on s

There is no (65, 199, 475)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 683247 845768 287009 462440 932315 431602 125119 012913 169164 576250 685782 288212 957702 749100 524780 693727 681915 105795 151804 651820 > 4¹⁹⁹ [i]