MinT - Best Known (63, 63+122, s)-Nets in Base 4

Best Known (63, 63+122, s)-Nets in Base 4

(63, 63+122, 66)-Net over F₄ — Constructive and digital

Digital (63, 185, 66)-net over F₄, using

t-expansion [i] based on digital (49, 185, 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]

(63, 63+122, 99)-Net over F₄ — Digital

Digital (63, 185, 99)-net over F₄, using

t-expansion [i] based on digital (61, 185, 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]

(63, 63+122, 477)-Net in Base 4 — Upper bound on s

There is no (63, 185, 478)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2560 629922 121987 884213 638011 826133 459922 905018 415469 573983 783086 531411 986190 276081 515653 195307 416902 104675 745450 > 4¹⁸⁵ [i]