MinT - Best Known (175−41, 175, s)-Nets in Base 4

Best Known (175−41, 175, s)-Nets in Base 4

(175−41, 175, 1036)-Net over F₄ — Constructive and digital

Digital (134, 175, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (134, 176, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 44, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(175−41, 175, 2283)-Net over F₄ — Digital

Digital (134, 175, 2283)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−41, 175, 478731)-Net in Base 4 — Upper bound on s

There is no (134, 175, 478732)-net in base 4, because

1 times m-reduction [i] would yield (134, 174, 478732)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 573 380542 576330 170117 281399 653324 543215 388936 774291 558276 033822 586046 003451 828496 385332 879785 640305 908544 > 4¹⁷⁴ [i]