MinT - Best Known (221−155, 221, s)-Nets in Base 4

Best Known (221−155, 221, s)-Nets in Base 4

(221−155, 221, 66)-Net over F₄ — Constructive and digital

Digital (66, 221, 66)-net over F₄, using

t-expansion [i] based on digital (49, 221, 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]

(221−155, 221, 99)-Net over F₄ — Digital

Digital (66, 221, 99)-net over F₄, using

t-expansion [i] based on digital (61, 221, 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]

(221−155, 221, 455)-Net in Base 4 — Upper bound on s

There is no (66, 221, 456)-net in base 4, because

1 times m-reduction [i] would yield (66, 220, 456)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 204525 702767 687462 929174 906902 387562 589825 439009 877613 563163 317635 643961 384866 396357 811131 106568 617030 217545 716902 036964 602343 820272 > 4²²⁰ [i]