MinT - Best Known (126, 233, s)-Nets in Base 4

Best Known (126, 233, s)-Nets in Base 4

(126, 233, 130)-Net over F₄ — Constructive and digital

Digital (126, 233, 130)-net over F₄, using

t-expansion [i] based on digital (105, 233, 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]

(126, 233, 215)-Net over F₄ — Digital

Digital (126, 233, 215)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 233, 2922)-Net in Base 4 — Upper bound on s

There is no (126, 233, 2923)-net in base 4, because

1 times m-reduction [i] would yield (126, 232, 2923)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48 400875 890876 803638 502402 231076 670294 122075 814138 860822 539597 822946 746960 218763 197587 110984 504528 041076 599743 146006 811978 747797 563166 282000 > 4²³² [i]