MinT - Best Known (137, 137+41, s)-Nets in Base 4

Best Known (137, 137+41, s)-Nets in Base 4

(137, 137+41, 1040)-Net over F₄ — Constructive and digital

Digital (137, 178, 1040)-net over F₄, using

4² times duplication [i] based on digital (135, 176, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 44, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(137, 137+41, 2531)-Net over F₄ — Digital

Digital (137, 178, 2531)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+41, 589391)-Net in Base 4 — Upper bound on s

There is no (137, 178, 589392)-net in base 4, because

1 times m-reduction [i] would yield (137, 177, 589392)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36696 399507 431507 921383 076608 635233 871441 646459 987734 699847 915434 308528 393417 321353 329851 155120 323736 539604 > 4¹⁷⁷ [i]