MinT - Best Known (111−46, 111, s)-Nets in Base 16

Best Known (111−46, 111, s)-Nets in Base 16

(111−46, 111, 532)-Net over F₁₆ — Constructive and digital

Digital (65, 111, 532)-net over F₁₆, using

1 times m-reduction [i] based on digital (65, 112, 532)-net over F₁₆, using
- trace code for nets [i] based on digital (9, 56, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(111−46, 111, 1120)-Net over F₁₆ — Digital

Digital (65, 111, 1120)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−46, 111, 406948)-Net in Base 16 — Upper bound on s

There is no (65, 111, 406949)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 45 428858 999470 524892 026424 873802 790842 827106 634565 114504 178725 122103 961788 980124 210774 255517 697910 920642 470788 693796 336336 901988 298656 > 16¹¹¹ [i]