MinT - Best Known (219−53, 219, s)-Nets in Base 4

Best Known (219−53, 219, s)-Nets in Base 4

(219−53, 219, 1032)-Net over F₄ — Constructive and digital

Digital (166, 219, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (166, 220, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 55, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(219−53, 219, 2340)-Net over F₄ — Digital

Digital (166, 219, 2340)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−53, 219, 392816)-Net in Base 4 — Upper bound on s

There is no (166, 219, 392817)-net in base 4, because

1 times m-reduction [i] would yield (166, 218, 392817)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 177455 370805 008980 855409 593115 621184 180191 815264 358963 538767 284913 346751 023156 399390 543664 572489 348210 666803 819347 527509 643137 660880 > 4²¹⁸ [i]