MinT - Best Known (254−123, 254, s)-Nets in Base 4

Best Known (254−123, 254, s)-Nets in Base 4

(254−123, 254, 130)-Net over F₄ — Constructive and digital

Digital (131, 254, 130)-net over F₄, using

t-expansion [i] based on digital (105, 254, 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]

(254−123, 254, 197)-Net over F₄ — Digital

Digital (131, 254, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−123, 254, 2417)-Net in Base 4 — Upper bound on s

There is no (131, 254, 2418)-net in base 4, because

1 times m-reduction [i] would yield (131, 253, 2418)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214 466148 971008 997761 300035 756269 890584 802378 642774 301494 153426 142652 523633 764081 158555 617184 645233 119104 422643 959220 671987 501034 652883 055663 180209 721200 > 4²⁵³ [i]