MinT - Best Known (144−35, 144, s)-Nets in Base 4

Best Known (144−35, 144, s)-Nets in Base 4

(144−35, 144, 1032)-Net over F₄ — Constructive and digital

Digital (109, 144, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 36, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(144−35, 144, 1617)-Net over F₄ — Digital

Digital (109, 144, 1617)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−35, 144, 277453)-Net in Base 4 — Upper bound on s

There is no (109, 144, 277454)-net in base 4, because

1 times m-reduction [i] would yield (109, 143, 277454)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 124 337835 453877 791139 747357 579419 232773 518250 280381 502248 627901 958449 115086 316422 719060 > 4¹⁴³ [i]