MinT - Best Known (63, 153, s)-Nets in Base 4

Best Known (63, 153, s)-Nets in Base 4

(63, 153, 66)-Net over F₄ — Constructive and digital

Digital (63, 153, 66)-net over F₄, using

t-expansion [i] based on digital (49, 153, 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, 153, 99)-Net over F₄ — Digital

Digital (63, 153, 99)-net over F₄, using

t-expansion [i] based on digital (61, 153, 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, 153, 618)-Net in Base 4 — Upper bound on s

There is no (63, 153, 619)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 134 944659 252325 811731 789595 708524 998946 208389 202898 140762 300764 635141 638004 619810 631524 751584 > 4¹⁵³ [i]