MinT - Best Known (76, 76+65, s)-Nets in Base 4

Best Known (76, 76+65, s)-Nets in Base 4

(76, 76+65, 104)-Net over F₄ — Constructive and digital

Digital (76, 141, 104)-net over F₄, using

t-expansion [i] based on digital (73, 141, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(76, 76+65, 137)-Net over F₄ — Digital

Digital (76, 141, 137)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+65, 1809)-Net in Base 4 — Upper bound on s

There is no (76, 141, 1810)-net in base 4, because

1 times m-reduction [i] would yield (76, 140, 1810)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 958029 408805 165968 062013 106118 415288 289640 429952 652876 099019 388429 722196 395584 402200 > 4¹⁴⁰ [i]