MinT - Best Known (234−109, 234, s)-Nets in Base 4

Best Known (234−109, 234, s)-Nets in Base 4

(234−109, 234, 130)-Net over F₄ — Constructive and digital

Digital (125, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(234−109, 234, 207)-Net over F₄ — Digital

Digital (125, 234, 207)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−109, 234, 2723)-Net in Base 4 — Upper bound on s

There is no (125, 234, 2724)-net in base 4, because

1 times m-reduction [i] would yield (125, 233, 2724)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 605860 223368 054870 303008 891009 858488 165245 017368 134190 197260 566877 139785 671664 683030 528150 366775 407679 428980 158865 297163 884502 581279 900320 > 4²³³ [i]