MinT - Best Known (238−57, 238, s)-Nets in Base 4

Best Known (238−57, 238, s)-Nets in Base 4

(238−57, 238, 1036)-Net over F₄ — Constructive and digital

Digital (181, 238, 1036)-net over F₄, using

4² times duplication [i] based on digital (179, 236, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 59, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(238−57, 238, 2648)-Net over F₄ — Digital

Digital (181, 238, 2648)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−57, 238, 469753)-Net in Base 4 — Upper bound on s

There is no (181, 238, 469754)-net in base 4, because

1 times m-reduction [i] would yield (181, 237, 469754)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48777 438409 254522 418165 687551 233987 215738 205287 292894 898674 831342 901446 383198 701985 609768 475939 670334 231462 001998 824342 095354 270731 644499 712968 > 4²³⁷ [i]