MinT - Best Known (133, 133+123, s)-Nets in Base 4

Best Known (133, 133+123, s)-Nets in Base 4

(133, 133+123, 130)-Net over F₄ — Constructive and digital

Digital (133, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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+123, 203)-Net over F₄ — Digital

Digital (133, 256, 203)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+123, 2531)-Net in Base 4 — Upper bound on s

There is no (133, 256, 2532)-net in base 4, because

1 times m-reduction [i] would yield (133, 255, 2532)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3371 589866 701951 075581 988204 362209 289209 207428 978326 736460 606898 505833 314441 636693 729199 964073 508467 042788 936727 673346 349672 335072 444757 285146 828119 841360 > 4²⁵⁵ [i]