MinT - Best Known (203−47, 203, s)-Nets in Base 4

Best Known (203−47, 203, s)-Nets in Base 4

(203−47, 203, 1040)-Net over F₄ — Constructive and digital

Digital (156, 203, 1040)-net over F₄, using

1 times m-reduction [i] based on digital (156, 204, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 51, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(203−47, 203, 2746)-Net over F₄ — Digital

Digital (156, 203, 2746)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−47, 203, 609507)-Net in Base 4 — Upper bound on s

There is no (156, 203, 609508)-net in base 4, because

1 times m-reduction [i] would yield (156, 202, 609508)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 316808 930757 215039 269813 677880 151249 550899 678100 934705 449492 272141 813128 344883 439042 340206 093481 649232 111669 220290 130680 > 4²⁰² [i]