MinT - Best Known (230−56, 230, s)-Nets in Base 4

Best Known (230−56, 230, s)-Nets in Base 4

(230−56, 230, 1032)-Net over F₄ — Constructive and digital

Digital (174, 230, 1032)-net over F₄, using

4² times duplication [i] based on digital (172, 228, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 57, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(230−56, 230, 2370)-Net over F₄ — Digital

Digital (174, 230, 2370)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−56, 230, 332159)-Net in Base 4 — Upper bound on s

There is no (174, 230, 332160)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 977251 135461 206166 644481 941052 925131 879330 289652 988330 391270 718939 437507 120116 305966 480478 771106 329531 568266 023131 702402 480639 392118 516457 > 4²³⁰ [i]