MinT - Best Known (142−67, 142, s)-Nets in Base 4

Best Known (142−67, 142, s)-Nets in Base 4

(142−67, 142, 104)-Net over F₄ — Constructive and digital

Digital (75, 142, 104)-net over F₄, using

t-expansion [i] based on digital (73, 142, 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]

(142−67, 142, 128)-Net over F₄ — Digital

Digital (75, 142, 128)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−67, 142, 1612)-Net in Base 4 — Upper bound on s

There is no (75, 142, 1613)-net in base 4, because

1 times m-reduction [i] would yield (75, 141, 1613)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 846634 226182 420605 118796 419604 077623 305585 654885 204136 201421 771888 593073 790472 747120 > 4¹⁴¹ [i]