MinT - Best Known (145−35, 145, s)-Nets in Base 4

Best Known (145−35, 145, s)-Nets in Base 4

(145−35, 145, 1032)-Net over F₄ — Constructive and digital

Digital (110, 145, 1032)-net over F₄, using

4¹ times duplication [i] based on 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]

(145−35, 145, 1684)-Net over F₄ — Digital

Digital (110, 145, 1684)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−35, 145, 301027)-Net in Base 4 — Upper bound on s

There is no (110, 145, 301028)-net in base 4, because

1 times m-reduction [i] would yield (110, 144, 301028)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 497 330591 785147 418592 034287 563185 158438 665600 496072 242540 334466 700279 126055 796673 964562 > 4¹⁴⁴ [i]