MinT - Best Known (247−133, 247, s)-Nets in Base 4

Best Known (247−133, 247, s)-Nets in Base 4

(247−133, 247, 130)-Net over F₄ — Constructive and digital

Digital (114, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(247−133, 247, 165)-Net over F₄ — Digital

Digital (114, 247, 165)-net over F₄, using

t-expansion [i] based on digital (109, 247, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(247−133, 247, 1432)-Net in Base 4 — Upper bound on s

There is no (114, 247, 1433)-net in base 4, because

1 times m-reduction [i] would yield (114, 246, 1433)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13239 234498 964820 365825 881249 421578 794949 439998 330197 900812 304952 264009 020753 461633 299753 296247 000946 056032 864890 330399 526197 635800 297931 793341 433000 > 4²⁴⁶ [i]