MinT - Best Known (66, 66+138, s)-Nets in Base 4

Best Known (66, 66+138, s)-Nets in Base 4

(66, 66+138, 66)-Net over F₄ — Constructive and digital

Digital (66, 204, 66)-net over F₄, using

t-expansion [i] based on digital (49, 204, 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]

(66, 66+138, 99)-Net over F₄ — Digital

Digital (66, 204, 99)-net over F₄, using

t-expansion [i] based on digital (61, 204, 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]

(66, 66+138, 477)-Net in Base 4 — Upper bound on s

There is no (66, 204, 478)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 661 760900 311967 189319 698346 675748 584719 797053 555435 915068 922191 328253 500905 852943 256613 025720 508010 900992 625295 659944 628659 > 4²⁰⁴ [i]