MinT - Best Known (124, 249, s)-Nets in Base 4

Best Known (124, 249, s)-Nets in Base 4

(124, 249, 130)-Net over F₄ — Constructive and digital

Digital (124, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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]

(124, 249, 173)-Net over F₄ — Digital

Digital (124, 249, 173)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 249, 1991)-Net in Base 4 — Upper bound on s

There is no (124, 249, 1992)-net in base 4, because

1 times m-reduction [i] would yield (124, 248, 1992)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 207055 610162 891029 323353 217077 505142 073128 125066 180849 207106 740431 929853 528205 913837 639155 565530 839281 957516 308139 767657 447597 082456 400709 101809 534120 > 4²⁴⁸ [i]