MinT - Best Known (64, 64+122, s)-Nets in Base 4

Best Known (64, 64+122, s)-Nets in Base 4

(64, 64+122, 66)-Net over F₄ — Constructive and digital

Digital (64, 186, 66)-net over F₄, using

t-expansion [i] based on digital (49, 186, 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]

(64, 64+122, 99)-Net over F₄ — Digital

Digital (64, 186, 99)-net over F₄, using

t-expansion [i] based on digital (61, 186, 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]

(64, 64+122, 489)-Net in Base 4 — Upper bound on s

There is no (64, 186, 490)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10165 270350 110990 209859 511172 756992 832238 617164 397720 673115 435456 145152 131290 958614 283337 113367 464600 304716 482288 > 4¹⁸⁶ [i]