MinT - Best Known (246−57, 246, s)-Nets in Base 4

Best Known (246−57, 246, s)-Nets in Base 4

(246−57, 246, 1044)-Net over F₄ — Constructive and digital

Digital (189, 246, 1044)-net over F₄, using

4² times duplication [i] based on digital (187, 244, 1044)-net over F₄, using
- trace code for nets [i] based on digital (4, 61, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(246−57, 246, 3221)-Net over F₄ — Digital

Digital (189, 246, 3221)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−57, 246, 698062)-Net in Base 4 — Upper bound on s

There is no (189, 246, 698063)-net in base 4, because

1 times m-reduction [i] would yield (189, 245, 698063)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3196 696433 432521 888372 101614 544045 207956 077648 696558 975959 873945 449831 470883 565957 509845 434656 293359 853158 980297 755330 054117 813921 386470 037526 942900 > 4²⁴⁵ [i]