MinT - Best Known (62, 62+128, s)-Nets in Base 4

Best Known (62, 62+128, s)-Nets in Base 4

(62, 62+128, 66)-Net over F₄ — Constructive and digital

Digital (62, 190, 66)-net over F₄, using

t-expansion [i] based on digital (49, 190, 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]

(62, 62+128, 99)-Net over F₄ — Digital

Digital (62, 190, 99)-net over F₄, using

t-expansion [i] based on digital (61, 190, 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]

(62, 62+128, 453)-Net in Base 4 — Upper bound on s

There is no (62, 190, 454)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 714365 738025 866464 303158 344441 611392 999094 452742 846644 055931 749327 522123 846187 017065 693983 477140 690463 971891 667915 > 4¹⁹⁰ [i]