MinT - Best Known (144−68, 144, s)-Nets in Base 4

Best Known (144−68, 144, s)-Nets in Base 4

(144−68, 144, 104)-Net over F₄ — Constructive and digital

Digital (76, 144, 104)-net over F₄, using

t-expansion [i] based on digital (73, 144, 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]

(144−68, 144, 130)-Net over F₄ — Digital

Digital (76, 144, 130)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−68, 144, 1572)-Net in Base 4 — Upper bound on s

There is no (76, 144, 1573)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 498 916142 680302 482227 936830 437648 972950 506515 254551 497027 518060 009399 650173 663956 918390 > 4¹⁴⁴ [i]