MinT - Best Known (234−115, 234, s)-Nets in Base 4

Best Known (234−115, 234, s)-Nets in Base 4

(234−115, 234, 130)-Net over F₄ — Constructive and digital

Digital (119, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(234−115, 234, 174)-Net over F₄ — Digital

Digital (119, 234, 174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−115, 234, 2081)-Net in Base 4 — Upper bound on s

There is no (119, 234, 2082)-net in base 4, because

1 times m-reduction [i] would yield (119, 233, 2082)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 194 814248 387830 635442 593248 095127 033654 895453 586331 463589 929676 252746 547555 484263 601738 205470 044858 851874 251705 014835 588695 248952 597142 073600 > 4²³³ [i]