MinT - Best Known (135, 135+123, s)-Nets in Base 4

Best Known (135, 135+123, s)-Nets in Base 4

(135, 135+123, 130)-Net over F₄ — Constructive and digital

Digital (135, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 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]

(135, 135+123, 209)-Net over F₄ — Digital

Digital (135, 258, 209)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+123, 2651)-Net in Base 4 — Upper bound on s

There is no (135, 258, 2652)-net in base 4, because

1 times m-reduction [i] would yield (135, 257, 2652)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53887 431451 326572 872828 239169 018237 703621 945828 846506 932976 774276 807846 831113 610063 739636 584036 930774 923394 756271 539011 442840 389194 664087 037520 913130 540720 > 4²⁵⁷ [i]