MinT - Best Known (207−49, 207, s)-Nets in Base 4

Best Known (207−49, 207, s)-Nets in Base 4

(207−49, 207, 1036)-Net over F₄ — Constructive and digital

Digital (158, 207, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (158, 208, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 52, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(207−49, 207, 2490)-Net over F₄ — Digital

Digital (158, 207, 2490)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−49, 207, 480734)-Net in Base 4 — Upper bound on s

There is no (158, 207, 480735)-net in base 4, because

1 times m-reduction [i] would yield (158, 206, 480735)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10577 061503 770713 842539 199651 236994 200090 152799 335752 851585 820580 536581 499821 768281 988502 246551 892000 809522 702784 787093 141379 > 4²⁰⁶ [i]