MinT - Best Known (65, 65+122, s)-Nets in Base 4

Best Known (65, 65+122, s)-Nets in Base 4

(65, 65+122, 66)-Net over F₄ — Constructive and digital

Digital (65, 187, 66)-net over F₄, using

t-expansion [i] based on digital (49, 187, 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]

(65, 65+122, 99)-Net over F₄ — Digital

Digital (65, 187, 99)-net over F₄, using

t-expansion [i] based on digital (61, 187, 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]

(65, 65+122, 501)-Net in Base 4 — Upper bound on s

There is no (65, 187, 502)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 39136 387796 601824 193750 737800 511137 096341 456087 291994 924996 305069 715873 426703 423497 401238 645895 799043 393149 457192 > 4¹⁸⁷ [i]