MinT - Best Known (248−111, 248, s)-Nets in Base 4

Best Known (248−111, 248, s)-Nets in Base 4

(248−111, 248, 130)-Net over F₄ — Constructive and digital

Digital (137, 248, 130)-net over F₄, using

t-expansion [i] based on digital (105, 248, 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]

(248−111, 248, 246)-Net over F₄ — Digital

Digital (137, 248, 246)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−111, 248, 3550)-Net in Base 4 — Upper bound on s

There is no (137, 248, 3551)-net in base 4, because

1 times m-reduction [i] would yield (137, 247, 3551)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51149 692853 311999 375695 855285 997591 708137 363437 618921 419877 481000 046732 329276 533958 602818 962220 158146 594513 922340 383384 231742 115252 172525 057768 148792 > 4²⁴⁷ [i]