MinT - Best Known (191−44, 191, s)-Nets in Base 4

Best Known (191−44, 191, s)-Nets in Base 4

(191−44, 191, 1040)-Net over F₄ — Constructive and digital

Digital (147, 191, 1040)-net over F₄, using

1 times m-reduction [i] based on digital (147, 192, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 48, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(191−44, 191, 2680)-Net over F₄ — Digital

Digital (147, 191, 2680)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−44, 191, 508969)-Net in Base 4 — Upper bound on s

There is no (147, 191, 508970)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 850626 082446 818558 222806 828636 768394 492343 013169 642729 866615 864517 332256 445293 141425 660654 320445 721231 493702 993304 > 4¹⁹¹ [i]