MinT - Best Known (149−35, 149, s)-Nets in Base 4

Best Known (149−35, 149, s)-Nets in Base 4

(149−35, 149, 1036)-Net over F₄ — Constructive and digital

Digital (114, 149, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (113, 148, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 37, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(149−35, 149, 1979)-Net over F₄ — Digital

Digital (114, 149, 1979)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−35, 149, 417131)-Net in Base 4 — Upper bound on s

There is no (114, 149, 417132)-net in base 4, because

1 times m-reduction [i] would yield (114, 148, 417132)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127316 394704 459201 768472 700762 665267 395062 866394 545520 621018 459517 005782 961671 296715 527230 > 4¹⁴⁸ [i]