MinT - Best Known (66, 207, s)-Nets in Base 4

Best Known (66, 207, s)-Nets in Base 4

(66, 207, 66)-Net over F₄ — Constructive and digital

Digital (66, 207, 66)-net over F₄, using

t-expansion [i] based on digital (49, 207, 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, 207, 99)-Net over F₄ — Digital

Digital (66, 207, 99)-net over F₄, using

t-expansion [i] based on digital (61, 207, 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, 207, 474)-Net in Base 4 — Upper bound on s

There is no (66, 207, 475)-net in base 4, because

1 times m-reduction [i] would yield (66, 206, 475)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11253 114151 736340 911031 915871 970435 422952 073011 089455 090215 947065 518536 025151 821297 576183 567968 358652 549778 754144 645749 729450 > 4²⁰⁶ [i]