MinT - Best Known (126, 126+95, s)-Nets in Base 4

Best Known (126, 126+95, s)-Nets in Base 4

(126, 126+95, 130)-Net over F₄ — Constructive and digital

Digital (126, 221, 130)-net over F₄, using

t-expansion [i] based on digital (105, 221, 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]

(126, 126+95, 253)-Net over F₄ — Digital

Digital (126, 221, 253)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+95, 3989)-Net in Base 4 — Upper bound on s

There is no (126, 221, 3990)-net in base 4, because

1 times m-reduction [i] would yield (126, 220, 3990)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 843792 593049 696000 486853 487766 931152 334952 184565 523913 976427 671551 139029 515337 594294 484914 545668 870637 740461 336391 171193 501108 500256 > 4²²⁰ [i]