MinT - Best Known (21, 21+28, s)-Nets in Base 4

Best Known (21, 21+28, s)-Nets in Base 4

(21, 21+28, 34)-Net over F₄ — Constructive and digital

Digital (21, 49, 34)-net over F₄, using

net from sequence [i] based on digital (21, 33)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
  - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(21, 21+28, 44)-Net over F₄ — Digital

Digital (21, 49, 44)-net over F₄, using

net from sequence [i] based on digital (21, 43)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 44, using
  - a curve from the manYPoints database [i]

(21, 21+28, 246)-Net in Base 4 — Upper bound on s

There is no (21, 49, 247)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 317356 997164 850748 033531 944854 > 4⁴⁹ [i]