MinT - Best Known (123, 123+105, s)-Nets in Base 4

Best Known (123, 123+105, s)-Nets in Base 4

(123, 123+105, 130)-Net over F₄ — Constructive and digital

Digital (123, 228, 130)-net over F₄, using

t-expansion [i] based on digital (105, 228, 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]

(123, 123+105, 209)-Net over F₄ — Digital

Digital (123, 228, 209)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+105, 2821)-Net in Base 4 — Upper bound on s

There is no (123, 228, 2822)-net in base 4, because

1 times m-reduction [i] would yield (123, 227, 2822)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46871 339946 277102 447345 973334 770280 067841 648908 976566 771129 031073 287298 978504 796417 595986 620038 378462 714937 235934 233112 990194 870250 775280 > 4²²⁷ [i]