MinT - Best Known (213−147, 213, s)-Nets in Base 4

Best Known (213−147, 213, s)-Nets in Base 4

(213−147, 213, 66)-Net over F₄ — Constructive and digital

Digital (66, 213, 66)-net over F₄, using

t-expansion [i] based on digital (49, 213, 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]

(213−147, 213, 99)-Net over F₄ — Digital

Digital (66, 213, 99)-net over F₄, using

t-expansion [i] based on digital (61, 213, 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]

(213−147, 213, 465)-Net in Base 4 — Upper bound on s

There is no (66, 213, 466)-net in base 4, because

1 times m-reduction [i] would yield (66, 212, 466)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 917832 918228 280025 085242 823750 023366 124908 452795 149977 297315 696930 468405 051226 768765 379124 787466 671806 699328 722519 473099 067270 > 4²¹² [i]