MinT - Best Known (65−42, 65, s)-Nets in Base 4

Best Known (65−42, 65, s)-Nets in Base 4

(65−42, 65, 34)-Net over F₄ — Constructive and digital

Digital (23, 65, 34)-net over F₄, using

t-expansion [i] based on digital (21, 65, 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]

(65−42, 65, 45)-Net over F₄ — Digital

Digital (23, 65, 45)-net over F₄, using

net from sequence [i] based on digital (23, 44)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 23 and N(F) ≥ 45, using
  - a curve from the manYPoints database [i]

(65−42, 65, 194)-Net in Base 4 — Upper bound on s

There is no (23, 65, 195)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1388 029327 848432 487461 678607 730009 340064 > 4⁶⁵ [i]