MinT - Best Known (178−43, 178, s)-Nets in Base 4

Best Known (178−43, 178, s)-Nets in Base 4

(178−43, 178, 1032)-Net over F₄ — Constructive and digital

Digital (135, 178, 1032)-net over F₄, using

4² times duplication [i] based on digital (133, 176, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 44, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(178−43, 178, 1981)-Net over F₄ — Digital

Digital (135, 178, 1981)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−43, 178, 343443)-Net in Base 4 — Upper bound on s

There is no (135, 178, 343444)-net in base 4, because

1 times m-reduction [i] would yield (135, 177, 343444)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36696 822392 356390 176885 873121 992126 636921 251642 549493 111079 397354 358582 066611 496161 434773 677542 844163 126592 > 4¹⁷⁷ [i]