MinT - Best Known (194−132, 194, s)-Nets in Base 4

Best Known (194−132, 194, s)-Nets in Base 4

(194−132, 194, 66)-Net over F₄ — Constructive and digital

Digital (62, 194, 66)-net over F₄, using

t-expansion [i] based on digital (49, 194, 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]

(194−132, 194, 99)-Net over F₄ — Digital

Digital (62, 194, 99)-net over F₄, using

t-expansion [i] based on digital (61, 194, 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]

(194−132, 194, 446)-Net in Base 4 — Upper bound on s

There is no (62, 194, 447)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 706 151799 223868 111541 088017 888532 875547 193491 695765 419508 554389 747434 545863 581322 942191 345710 234141 517106 334307 340666 > 4¹⁹⁴ [i]