MinT - Best Known (133, 133+103, s)-Nets in Base 4

Best Known (133, 133+103, s)-Nets in Base 4

(133, 133+103, 130)-Net over F₄ — Constructive and digital

Digital (133, 236, 130)-net over F₄, using

t-expansion [i] based on digital (105, 236, 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]

(133, 133+103, 255)-Net over F₄ — Digital

Digital (133, 236, 255)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+103, 3893)-Net in Base 4 — Upper bound on s

There is no (133, 236, 3894)-net in base 4, because

1 times m-reduction [i] would yield (133, 235, 3894)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3085 950517 615276 624933 514323 813516 696898 747485 072622 485750 915121 644466 024723 950407 552659 953185 386786 045373 611928 933789 937823 161673 185003 690318 > 4²³⁵ [i]