MinT - Best Known (248−123, 248, s)-Nets in Base 4

Best Known (248−123, 248, s)-Nets in Base 4

(248−123, 248, 130)-Net over F₄ — Constructive and digital

Digital (125, 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]

(248−123, 248, 178)-Net over F₄ — Digital

Digital (125, 248, 178)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−123, 248, 2102)-Net in Base 4 — Upper bound on s

There is no (125, 248, 2103)-net in base 4, because

1 times m-reduction [i] would yield (125, 247, 2103)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51667 086814 666685 015615 406011 061459 039224 206914 821665 186204 327858 009961 976966 304651 552141 642050 856064 275282 618639 418049 697089 801495 794597 607091 571200 > 4²⁴⁷ [i]